1. Distance and Mid point

2. Quick review: The coordinate plane
4 Quadrants
X axis, horizontal
Y axis, vertical
Plotting point (3, -2)
start at origin (0,0)
x, go left (-) or right (+)
y, go up(+) or down(-) II I
III IV
(3, -2)

3. Line Segment vs Line Iines go on forever, arrows on each end
Line segments have end points
The length of a line segment is the distance between the two endpoints
Often the end points are assigned letters
(4,3) B A
(-4,-4)

4. Length of a Line Segment
What is the length of this line segment?
Count the spaces from one end point to the other
(4,3) B
7 units A
(4,-4)

5. Length of a Line Segment
What about the length of this one?
Count the spaces from one end point to the other
6 units
(-2,-3) A B
(4,-4)

6. Length of a Line Segment
When the line segment is like this, it is not so easy to find the exact length.
Just for kicks, estimate how long you think it is
About 8? 9?
To find this exact length we use the distance formula
(4,3) B A
(-4,-4)

7. Distance Formula
Used to find the distance between two points

8. Example
Find the distance between A(-4,-4) and B(4,3)
A (-4, -4)
B (4, 3)

9. Example
Find the distance between A(-4,-4) and B(4,3)
A (-4, -4)
B (4, 3)

10. YOU TRY!! Find the distance between: A. (2, 7) and (11, 9)
B. (-5, 8) and (2, - 4)

11. Distance Vs Midpoint Distance is the length between two points
Midpoint is the point that is exactly half way between two points.
9.21 units
(.5,0)

12. Midpoint Formula
Used to find the center of a line segment

13. Example
Find the midpoint between A(4,8) and B(1,12)
A (4, 8)
B (1, 12)

14. SAD STACKER A way to remember the midpoint formula
Find the midpoint between A(4,8) and B(1,12)
(4 , 8 )
(1, 12)
(5, 20)
2 2
(2.5, 10)
Stack em
Add em
Divide by 2

15. YOU TRY!! Find the midpoint between: A) (2, 7) and (14, 9)
B) (-5, 8) and (2, - 4)